Guess Game Logic Problem

Mind Teasers :
Guess Game Logic Problem

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In a guess game , five friends had to guess the exact numbers of balls in a box.
Friends guessed as 31 , 35, 39 , 49 , 37, but none of guess was right.The guesses were off by 1, 9, 5, 3, and 9 (in a random order).
Can you determine the number of balls in a box ?

The number of decks is absolutely not relevant here which means whether we mix 5 or 500 cards still results would be same.
Any card drawn will be a Ace,2,3,4,5,6,7,8,9,10,Jack,Queen or King, so there are 13 possibilities each time a card is drawn.
If you are lucky just 5 cards of the same kind can be obtained in 4 steps

The unluckiest(worst) way is our solution as we need to guarantee a four of a kind.
Draw 3 of each kind =>now we have 39 cards. Next card will guarantee 4 of a kind.

n a hotel, a man was sleeping when he heard a knock on the door. He shifted the blanket and stepped down from the bed. He waked to the door and opened it to find a stranger standing outside.
Upon opening the gate, that stranger said, "Pardon me, I must have made a mistake. I thought this was my room."
The stranger then walked the corridor and climbed down the stairs. The man closed the door and immediately called the security. He asked them to arrest that stranger immediately.
Why did he asked them to arrest that stranger? What made him suspicious?

A petri dish kept in a lab has a colony of healthy bacteria. Every bacterium divides itself into two in exactly two minutes. Now the colony started with a single cell at 2 pm. If the petri dish was exactly half full of bacteria at 3 pm, when will the dish become full of bacteria?

Since every bacterium divides into two in two minutes and we know the fact that the dish was half filled with bacteria at 3 pm, after exactly 2 minutes, all will divide into two and will fill the petri dish. Thus, the petri dish will become full at 3:02 pm.

One is if I run on the perimeter. Then, the lion will eventually catch me as the lion can follow my radius and then his trajectory will be half of the circle and not a spiral. Therefore, the lion will subsequently catch me in a finite amount of time.

Secondly if I don’t run on the perimeter, then clearly, I have an infinite amount of time before the lion catches me.

A person has uncovered a secret that was a mystery for ages. He transfers the data into his hard drive and encrypts the drive with a password. Then, he writes a line on a paper to remember the password.

The line says 'You force heaven to be empty'.

Can you decrypt the line to reveal the password if you know that the password is seven characters long that comprise of just letters and numbers?